High-dimensional Private Quantum Channels and Regular Polytopes

Junseo Lee, Kabgyun Jeong
Author affiliations

Authors

  • Junseo Lee School of Electrical and Electronic Engineering, Yonsei University, Seoul 03722, Korea
  • Kabgyun Jeong Research Institute of Mathematics, Seoul National University, Seoul 08826, Korea and School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea

DOI:

https://doi.org/10.15625/0868-3166/15762

Abstract

As the quantum analog of the classical one-time pad, the private quantum channel (PQC) plays a fundamental role in the construction of the maximally mixed state (from any input quantum state), which is very useful for studying secure quantum communications and quantum channel capacity problems. However, the undoubted existence of a relation between the geometric shape of regular polytopes and private quantum channels in the higher dimension has not yet been reported. Recently, it was shown that a one-to-one correspondence exists between single-qubit PQCs and three-dimensional regular polytopes (i.e., regular polyhedra). In this paper, we highlight these connections by exploiting two strategies known as a generalized Gell-Mann matrix and modified quantum Fourier transform. More precisely, we explore the explicit relationship between PQCs over a qutrit system (i.e., a three-level quantum state) and regular 4-polytopes. Finally, we attempt to devise a formula for such connections on higher dimensional cases.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

10-05-2021

How to Cite

[1]
J. Lee and K. Jeong, “High-dimensional Private Quantum Channels and Regular Polytopes”, Comm. Phys., vol. 31, no. 2, p. 189, May 2021.

Issue

Section

Papers
Received 16-12-2020
Accepted 02-01-2021
Published 10-05-2021